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| CMS-PAS-HIG-17-031 | ||
| Combined measurements of the Higgs boson's couplings at $\sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| March 2018 | ||
| Abstract: Combined measurements of the Higgs boson's production and decay rates, as well its couplings to vector bosons and fermions, are presented. The analysis uses the LHC proton-proton collision data set recorded by the CMS detector in 2016 at $\sqrt{s}= $ 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The combination is based on the analysis of the production processes gluon fusion, vector boson fusion, and associated production with a W or Z boson or a pair of top quarks, and of the H$\to$ZZ, WW, $\gamma\gamma$, $\tau\tau$, bb, and $\mu\mu$ decay modes. Dedicated searches for invisible Higgs boson decays are also considered. The combined signal strength is measured as $\mu= $ 1.17$^{+0.10}_{-0.10}$. The Higgs boson production and decay rates are combined within the context of two generic parameterizations: one based on the ratios of cross sections and branching ratios, and the other based on the ratios of coupling modifiers. Several interpretations of the results, with more model-dependent parameterizations derived from the generic ones, are also given. The results are compatible with the standard model predictions in all of the parameterizations considered. The results are used to place constraints on the parameter spaces of various two Higgs doublet models. | ||
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Links:
CDS record (PDF) ;
inSPIRE record ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, EPJC 79 (2019) 421. The superseded preliminary plots can be found here. |
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| Figures | |
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Figure 1:
Examples of leading order Feynman diagrams for the (a) ${{\mathrm {g}} {\mathrm {g}} {\mathrm {H}}}$, (b) ${\mathrm {VBF}}$, (c) ${\mathrm {V} {\mathrm {H}}}$, and (d) ${{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}}$ production modes. |
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Figure 1-a:
Example of leading order Feynman diagram for the ${{\mathrm {g}} {\mathrm {g}} {\mathrm {H}}}$ production mode. |
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Figure 1-b:
Example of leading order Feynman diagram for the ${\mathrm {VBF}}$, (c) ${\mathrm {V} {\mathrm {H}}}$ production mode. |
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Figure 1-c:
Example of leading order Feynman diagram for the ${{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}}$ production mode. |
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Figure 1-d:
Examples of leading order Feynman diagrams for the (a) ${{\mathrm {g}} {\mathrm {g}} {\mathrm {H}}}$, (b) ${\mathrm {VBF}}$, (c) ${\mathrm {V} {\mathrm {H}}}$, and (d) ${{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}}$ production modes. |
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Figure 2:
Examples of leading order Feynman diagrams for the $\text {gg}\to {{\mathrm {Z}} {\mathrm {H}}} $ production mode. |
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Figure 2-a:
Example of leading order Feynman diagram for the $\text {gg}\to {{\mathrm {Z}} {\mathrm {H}}} $ production mode. |
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Figure 2-b:
Example of leading order Feynman diagram for the $\text {gg}\to {{\mathrm {Z}} {\mathrm {H}}} $ production mode. |
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Figure 3:
Examples of leading order Feynman diagrams for ${{\mathrm {t}} {\mathrm {H}}}$ production via the (a,b) ${{\mathrm {t}} {\mathrm {H}} {\mathrm {W}}}$ and (c) ${{\mathrm {t}} {\mathrm {H}} \mathrm{q}}$ modes. |
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Figure 3-a:
Example of leading order Feynman diagram for ${{\mathrm {t}} {\mathrm {H}}}$ production via the ${{\mathrm {t}} {\mathrm {H}} {\mathrm {W}}}$ mode. |
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Figure 3-b:
Example of leading order Feynman diagram for ${{\mathrm {t}} {\mathrm {H}}}$ production via the ${{\mathrm {t}} {\mathrm {H}} {\mathrm {W}}}$ mode. |
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Figure 3-c:
Example of leading order Feynman diagram for ${{\mathrm {t}} {\mathrm {H}}}$ production via the ${{\mathrm {t}} {\mathrm {H}} \mathrm{q}}$ mode. |
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Figure 4:
Examples of leading order Feynman diagrams for Higgs boson decay in the (a) bb, $\tau \tau$ and $\mu \mu$, (b) ZZ and WW, (c,d) $\gamma \gamma $ channels. |
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Figure 4-a:
Example of leading order Feynman diagram for Higgs boson decay in the bb, $\tau \tau$ and $\mu \mu$ channels. |
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Figure 4-b:
Example of leading order Feynman diagram for Higgs boson decay in the ZZ and WW channels. |
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Figure 4-c:
Example of leading order Feynman diagram for Higgs boson decay in the $\gamma \gamma $ channel. |
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Figure 4-d:
Example of leading order Feynman diagram for Higgs boson decay in the $\gamma \gamma $ channel. |
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Figure 5:
Summary plot of the fit to the per-production mode (left) and per-decay mode (right) signal strength modifiers $\mu _i$. The thick and thin horizontal bars indicate the $ \pm $1$ \sigma $ and $ \pm $2$ \sigma $ uncertainties, respectively. Also shown are the $ \pm $1$ \sigma $ systematic components of the uncertainties. The last point in the per-production mode summary plot is taken from a separate fit and indicates the result of the combined overall signal strength $\mu $. |
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Figure 5-a:
Summary plot of the fit to the per-production mode signal strength modifiers $\mu _i$. The thick and thin horizontal bars indicate the $ \pm $1$ \sigma $ and $ \pm $2$ \sigma $ uncertainties, respectively. Also shown are the $ \pm $1$ \sigma $ systematic components of the uncertainties. The last point is taken from a separate fit and indicates the result of the combined overall signal strength $\mu $. |
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Figure 5-b:
Summary plot of the fit to the per-decay mode signal strength modifiers $\mu _i$. The thick and thin horizontal bars indicate the $ \pm $1$ \sigma $ and $ \pm $2$ \sigma $ uncertainties, respectively. Also shown are the $ \pm $1$ \sigma $ systematic components of the uncertainties. |
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Figure 6:
Summary plot of the fit to the production-decay signal strength products $\mu _{i}^{f}=\mu _{i}\times \mu ^{f}$. The points indicate the best-fit values while the horizontal bars indicate the 1$\sigma $ CL intervals. The hatched areas indicate signal strengths which are restricted to positive values due to low background contamination. |
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Figure 7:
Summary of the cross section and branching fraction ratio model. The thick and thin horizontal bars indicate the $ \pm $1$ \sigma $ and $ \pm $2$ \sigma $ uncertainties, respectively. Also shown are the $ \pm $1$ \sigma $ systematic components of the uncertainties. |
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Figure 8:
Summary of the stage 0 model, ratios of cross sections and branching ratios. The points indicate the best-fit values while the error bars show the $ \pm $1$ \sigma $ and $ \pm $2$ \sigma $ uncertainties. Also shown are the $ \pm $1$ \sigma $ uncertainties on the measurements considering only the contributions from the systematic uncertainties. Also shown are the uncertainties on the SM predictions. |
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Figure 9:
Summary of the $\kappa $-framework model with $ {\mathrm {BR_{BSM}}} = $ 0. The points indicate the best-fit values while the thick and thin horizontal bars show the 1$\sigma $ and 2$\sigma $ CL intervals, respectively. In this model, the ${{\mathrm {g}} {\mathrm {g}} {\mathrm {H}}} $ and ${{\mathrm {H}} \to {\gamma \gamma}} $ loops are resolved in terms of the remaining coupling modifiers. For this model, both positive and negative values of $\kappa _{{\mathrm {Z}}}$ and $\kappa _{\mathrm{b}}$ are considered while $\kappa _{{\mathrm {W}}}$ is assumed to be positive. |
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Figure 10:
Left: Likelihood scan in the $\rm{M}$-$\epsilon$ plane. The best-fit point and, 1$\sigma$, 2$\sigma$ CL regions are shown, along with the SM prediction. Right: Result of the phenomenological M, $\epsilon$ fit overlayed with the resolved $\kappa$-framework model. |
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Figure 10-a:
Likelihood scan in the $\rm{M}$-$\epsilon$ plane. The best-fit point and, 1$\sigma$, 2$\sigma$ CL regions are shown, along with the SM prediction. |
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Figure 10-b:
Result of the phenomenological M, $\epsilon$ fit overlayed with the resolved $\kappa$-framework model. |
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Figure 11:
Summary plots of the $\kappa $-framework model in which the ${{\mathrm {g}} {\mathrm {g}} {\mathrm {H}}} $ and ${{\mathrm {H}} \to {\gamma \gamma}} $ loops are scaled with effective couplings. The points indicate the best-fit values while the thick and thin horizontal bars show the 1$\sigma $ and 2$\sigma $ CL intervals, respectively. For the summary plot on the left the constraint $ {\mathrm {BR_{BSM}}} = $ 0 is imposed, and both positive and negative values of $\kappa _{{\mathrm {Z}}}$ are considered while $\kappa _{{\mathrm {W}}}$ is assumed to be positive. For the summary plot on the right, both $\kappa _{{\mathrm {W}}}$ and $\kappa _{{\mathrm {Z}}}$ are assumed to be positive with the constraint $|\kappa _{{\mathrm {W}}}|, |\kappa _{{\mathrm {Z}}}|\le $ 1, while $ {\mathrm {BR_{inv.}}} > $ 0 and $ {\mathrm {BR_{undet.}}} > $ 0 are free parameters. |
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Figure 11-a:
Summary plot of the $\kappa $-framework model in which the ${{\mathrm {g}} {\mathrm {g}} {\mathrm {H}}} $ and ${{\mathrm {H}} \to {\gamma \gamma}} $ loops are scaled with effective couplings. The points indicate the best-fit values while the thick and thin horizontal bars show the 1$\sigma $ and 2$\sigma $ CL intervals, respectively. The constraint $ {\mathrm {BR_{BSM}}} = $ 0 is imposed, and both positive and negative values of $\kappa _{{\mathrm {Z}}}$ are considered while $\kappa _{{\mathrm {W}}}$ is assumed to be positive. |
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Figure 11-b:
Summary plot of the $\kappa $-framework model in which the ${{\mathrm {g}} {\mathrm {g}} {\mathrm {H}}} $ and ${{\mathrm {H}} \to {\gamma \gamma}} $ loops are scaled with effective couplings. The points indicate the best-fit values while the thick and thin horizontal bars show the 1$\sigma $ and 2$\sigma $ CL intervals, respectively. Both $\kappa _{{\mathrm {W}}}$ and $\kappa _{{\mathrm {Z}}}$ are assumed to be positive with the constraint $|\kappa _{{\mathrm {W}}}|, |\kappa _{{\mathrm {Z}}}|\le $ 1, while $ {\mathrm {BR_{inv.}}} > $ 0 and $ {\mathrm {BR_{undet.}}} > $ 0 are free parameters. |
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Figure 12:
Scans of $q$ as a function of $ {\mathrm {BR_{inv.}}} $ (left), and 68% and 95% CL regions for $ {\mathrm {BR_{inv.}}} $ vs $ {\mathrm {BR_{undet.}}} $ (right), in the model where only positive values of $\kappa _{\rm V}$ (same sign of $\kappa _{{\mathrm {W}}}$ and $\kappa _{{\mathrm {Z}}}$) are considered with the constraint $|\kappa _{{\mathrm {W}}}|, |\kappa _{{\mathrm {Z}}}|\le $ 1, and $ {\mathrm {BR_{inv.}}} > $ 0 and $ {\mathrm {BR_{undet.}}} > $ 0 are free parameters. The scan of $q$ as a function of $ {\mathrm {BR_{inv.}}} $ expected assuming the SM is also shown in the left panel. |
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Figure 12-a:
Scans of $q$ as a function of $ {\mathrm {BR_{inv.}}} $, in the model where only positive values of $\kappa _{\rm V}$ (same sign of $\kappa _{{\mathrm {W}}}$ and $\kappa _{{\mathrm {Z}}}$) are considered with the constraint $|\kappa _{{\mathrm {W}}}|, |\kappa _{{\mathrm {Z}}}|\le $ 1, and $ {\mathrm {BR_{inv.}}} > $ 0 and $ {\mathrm {BR_{undet.}}} > $ 0 are free parameters. The scan of $q$ as a function of $ {\mathrm {BR_{inv.}}} $ expected assuming the SM is also shown. |
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Figure 12-b:
68% and 95% CL regions for $ {\mathrm {BR_{inv.}}} $ vs $ {\mathrm {BR_{undet.}}} $, in the model where only positive values of $\kappa _{\rm V}$ (same sign of $\kappa _{{\mathrm {W}}}$ and $\kappa _{{\mathrm {Z}}}$) are considered with the constraint $|\kappa _{{\mathrm {W}}}|, |\kappa _{{\mathrm {Z}}}|\le $ 1, and $ {\mathrm {BR_{inv.}}} > $ 0 and $ {\mathrm {BR_{undet.}}} > $ 0 are free parameters. |
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Figure 13:
Scans of $q$ as a function of $\Gamma _{\rm {H}}/\Gamma _{\rm {H}}^{\rm {SM}}$ obtained by reinterpreting the model allowing for BSM decays of the Higgs boson. |
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Figure 14:
The 1$\sigma $ and 2$\sigma $ CL regions in the $\kappa _{g}$ vs $\kappa _{\gamma}$ parameter space for the model assuming the only BSM contributions to the Higgs boson couplings appear in the loop-induced processes or in BSM Higgs decays. |
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Figure 15:
Summary of the model with coupling ratios and effective couplings for the ${{\mathrm {g}} {\mathrm {g}} {\mathrm {H}}}$ and ${{\mathrm {H}} \to {\gamma \gamma}}$ loops. The points indicate the best-fit values while the thick and thin horizontal bars show the 1$\sigma $ and 2$\sigma $ CL intervals, respectively. For this model, both positive and negative values of $\lambda _{\rm {WZ}}$ and $\lambda _{\mathrm{t} {\mathrm {g}}}$ are considered. |
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Figure 16:
The 1$\sigma $ and 2$\sigma $ CL regions in the $\kappa _{\rm {F}}$ vs $\kappa _{\rm {V}}$ parameter space for the model assuming a common scaling of all the vector boson and fermion couplings. |
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Figure 17:
Summary plots of the 3-parameter models comparing up- and down-type fermions, and floating the ratio of the vector coupling to the up-type coupling (left) and comparing lepton and quark couplings (right). The points indicate the best-fit values while the thick and thin horizontal bars show the $1\sigma $ and 2$\sigma $ CL intervals, respectively. Both positive and negative values of $\lambda _{\rm {du}}$, $\lambda _{\rm {Vu}}$, $\lambda _{\rm {lq}}$, and $\lambda _{\rm {Vq}}$ are considered. |
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Figure 17-a:
Summary plot of the 3-parameter models comparing up- and down-type fermions, and floating the ratio of the vector coupling to the up-type coupling. The points indicate the best-fit values while the thick and thin horizontal bars show the $1\sigma $ and 2$\sigma $ CL intervals, respectively. Both positive and negative values of $\lambda _{\rm {du}}$, $\lambda _{\rm {Vu}}$ are considered. |
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Figure 17-b:
Summary plot of the 3-parameter models comparing lepton and quark couplings (right). The points indicate the best-fit values while the thick and thin horizontal bars show the $1\sigma $ and 2$\sigma $ CL intervals, respectively. Both positive and negative values of $\lambda _{\rm {lq}}$, and $\lambda _{\rm {Vq}}$ are considered. |
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Figure 18:
Constraints in the $\cos({\beta -\alpha})-\tan\beta $ plane for the (a) Type I, (b) Type II, (c) Type III, (d) Type IV 2HDM. (e) Constraints in the $m_{\mathrm {A}}-\tan\beta $ plane for the hMSSM. The white regions, bounded by the solid black lines, in each plane represents the regions of the parameter space which are allowed at the 95% CL, given the data observed. The dashed lines indicate the boundaries of the allowed regions expected for the SM Higgs boson. |
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Figure 18-a:
Constraints in the $\cos({\beta -\alpha})-\tan\beta $ plane for the Type I 2HDM. The white regions, bounded by the solid black lines, represents the regions of the parameter space which are allowed at the 95% CL, given the data observed. The dashed lines indicate the boundaries of the allowed regions expected for the SM Higgs boson. |
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Figure 18-b:
Constraints in the $\cos({\beta -\alpha})-\tan\beta $ plane for the Type II 2HDM. The white regions, bounded by the solid black lines, represents the regions of the parameter space which are allowed at the 95% CL, given the data observed. The dashed lines indicate the boundaries of the allowed regions expected for the SM Higgs boson. |
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Figure 18-c:
Constraints in the $\cos({\beta -\alpha})-\tan\beta $ plane for the Type III 2HDM. The white regions, bounded by the solid black lines, represents the regions of the parameter space which are allowed at the 95% CL, given the data observed. The dashed lines indicate the boundaries of the allowed regions expected for the SM Higgs boson. |
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Figure 18-d:
Constraints in the $\cos({\beta -\alpha})-\tan\beta $ plane for the Type IV 2HDM. The white regions, bounded by the solid black lines, represents the regions of the parameter space which are allowed at the 95% CL, given the data observed. The dashed lines indicate the boundaries of the allowed regions expected for the SM Higgs boson. |
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Figure 18-e:
Constraints in the $m_{\mathrm {A}}-\tan\beta $ plane for the hMSSM. The white regions, bounded by the solid black lines, represents the regions of the parameter space which are allowed at the 95% CL, given the data observed. The dashed lines indicate the boundaries of the allowed regions expected for the SM Higgs boson. |
| Tables | |
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Table 1:
Summary of the channels in the analyses included in this combination. The first and second columns indicate which decay mode and/or production mechanism are targeted by an analysis. |
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Table 2:
Compatibility of the fit results with the SM prediction under various signal parameterizations. The value of $q$ at the values of the parameters of interest for which the SM expectation is obtained ($q_{\text {SM}}$) is shown along with the corresponding $p$-value, with respect to the SM, assuming $q$ is distributed according to a $\chi ^{2}$ function with the specified number of degrees of freedom (DOF). |
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Table 3:
Best-fit values and $ \pm $1$ \sigma $ uncertainties for the parameters of the models with per-production mode and per-decay mode signal strength modifiers. The expected uncertainties are given in brackets. |
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Table 4:
Best-fit values and $ \pm $1$ \sigma $ uncertainties for the parameters of the model with one signal strength parameter for each production and decay mode combination. The entries in the table represent the parameter $\mu _{i}^{f}=\mu _{i}\times \mu ^{f}$, where $i$ is indicated by the row and $f$ by the column. The expected uncertainties are given in brackets. Some of the signal strengths are restricted to positive values, as described in the text. |
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Table 5:
Best-fit values and $ \pm $1$ \sigma $ uncertainties for the parameters of the cross section and branching fraction ratio model. The expected uncertainties are given in brackets. |
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Table 6:
Best-fit values and $ \pm $1$ \sigma $ uncertainties for the parameters of the stage 0 simplified template cross section model. The values are all normalized to the SM predictions. The expected uncertainties are given in brackets. |
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Table 7:
Normalization scaling factors for all relevant production cross sections and decay partial widths. For those $\kappa $ parameters representing loop processes, the resolved scaling in terms of the fundamental SM couplings are also given. |
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Table 8:
Best-fit values and $ \pm $1$ \sigma $ uncertainties for the parameters of the $\kappa $ model in which the loop processes are resolved. The expected uncertainties are given in brackets. |
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Table 9:
Best-fit values and $ \pm $1$ \sigma $ uncertainties for the parameters of the $\kappa $-framework model with effective loops. The expected uncertainties are given in brackets. |
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Table 10:
Best-fit values and $ \pm $1$ \sigma $ uncertainties for the parameters of the coupling modifier ratio model. The expected uncertainties are given in brackets. |
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Table 11:
Best-fit values and $ \pm $1$ \sigma $ uncertainties for the parameters of the $\kappa _{\rm {V}},\kappa _{\rm {F}}$ model. The expected uncertainties are given in brackets. |
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Table 12:
Best-fit values and $ \pm $1$ \sigma $ uncertainties for the parameters of the benchmark models with resolved loops to test the symmetry of fermion couplings. The expected uncertainties are given in brackets. |
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Table 13:
Modifications to the couplings of the Higgs bosons to up-type ($\kappa _{u}$) and down-type ($\kappa _{d}$) fermions, and vector bosons ($\kappa _{V}$), with respect to the SM expectation, in 2HDM and for the hMSSM. The coupling modifications for the hMSSM are completed by the expressions for $s_{u}$ and $s_{d}$, as given in Equation xxxxx. |
| Summary |
|
A set of combined measurements of the Higgs boson's production and decay rates has been presented, along with the consequential constraints placed on its couplings to standard model (SM) particles, and on the parameter spaces of several beyond the standard model (BSM) scenarios. The combination is based on analyses targeting the gluon fusion (${\mathrm{g}\mathrm{g}\mathrm{H}} $), vector boson fusion production modes, and associated production with a vector boson or a pair of top quarks. The analyses included in the combination target Higgs boson decay in one of the $\mathrm{H} \to \mathrm{Z}\mathrm{Z}$, $\mathrm{W}\mathrm{W}$, $\gamma\gamma$, $\tau\tau$, bb, and $\mu\mu$ channels, using 35.9 fb$^{-1}$ of 13 TeV proton-proton collision data. Additionally, searches for invisible Higgs boson decays are included to increase the sensitivity to potential interactions with BSM particles. Measurements of the Higgs boson production cross section times branching ratio, in each of the channels are presented, along with a generic parameterization in terms of ratios of production cross sections and branching ratios, which makes no assumptions about the Higgs boson's total width. The combined signal yield relative to the SM prediction has been measured as $1.17^{+0.10}_{-0.10}$. Improvements in the precision of the ${\mathrm{g}\mathrm{g}\mathrm{H}} $ production rate of around $\sim$50% is achieved compared to previous ATLAS and CMS measurements. Additionally, a set of measurements of fiducial cross sections of Higgs boson processes, in the context of the simplified template cross sections, are presented for the first time from a combination of five decay channels. Furthermore, interpretations are provided in the context of a LO coupling modifier framework, including variants for which effective couplings to the photon and gluon are introduced. All of the results presented are compatible with the SM prediction, and the invisible branching ratio of the Higgs boson is constrained to be less than 22% at 95% CL. The results are additionally interpreted in two BSM models, the minimal supersymmetric model and the generic two Higgs doublet model. The constraints placed in the parameter spaces of these models are complementary to those which can be obtained from direct searches for additional Higgs bosons. |
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